Question: Rewrite the function by completing the square. $f(x)=x^{2}+14x+8$ $f(x)=(x+$
Answer: We want to complete $x^2{+14}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+14}}{2}\right)^2={49}$ to it: $x^2{+14}x+{49}=(x+7)^2$ In order to keep the expression equivalent, we add and subtract ${49}$, not forgetting the expression's constant term, $8$ : $\begin{aligned} f(x)&=x^2+14x+8 \\\\ &=x^2+14x+{49}+8-{49} \\\\ &=(x+7)^2+8-49 \\\\ &=(x+7)^2-41 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 7)^2 - 41$